Melt 2 tablespoons of the butter or margarine in a saucepan. Add mushrooms, celery, onion, green pepper and basil. Sauté for about 10 minutes or until celery is tender. While mushrooms are sautéing, make sauce by melting 4 tablespoons of butter or margarine in the top of a double boiler. Stirring constantly, gradually add the flour. Add salt, pepper and nutmeg. Slowly pour in milk. Cook and stir for about 6 minutes until sauce is thick and smooth. Add skate to mushroom mixture and cook for about 5 minutes. Combine skate and mushroom mixture with the white sauce and stir well. Pour mixture into a casserole dish. Cover with cracker crumbs and top with grated cheddar cheese. Bake for approximately 20 minutes at 350°F or until casserole is golden brown.